Local mean dimension theory for sofic group actions
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929501059940352 |
|---|---|
| author | García-Ramos, Felipe Gutman, Yonatan |
| author_facet | García-Ramos, Felipe Gutman, Yonatan |
| contents | Using a local perspective, we introduce \textit{mean dimension pairs} and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group $G$ has positive mean dimension. In addition we show that the mean dimension map is Borel, and that the set of subshifts with completely positive mean dimension of $[0,1]^G$, the full $G$-shift on the interval, is a complete coanalytic set in the set of all subshifts (hence not Borel). Our results are new even when the acting group is $\Z$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local mean dimension theory for sofic group actions García-Ramos, Felipe Gutman, Yonatan Dynamical Systems 37B05, 37B40, 54H05 Using a local perspective, we introduce \textit{mean dimension pairs} and give sufficient conditions of when every non-trivial factor of a continuous group action of a sofic group $G$ has positive mean dimension. In addition we show that the mean dimension map is Borel, and that the set of subshifts with completely positive mean dimension of $[0,1]^G$, the full $G$-shift on the interval, is a complete coanalytic set in the set of all subshifts (hence not Borel). Our results are new even when the acting group is $\Z$. |
| title | Local mean dimension theory for sofic group actions |
| topic | Dynamical Systems 37B05, 37B40, 54H05 |
| url | https://arxiv.org/abs/2401.08440 |